The scattering of charged mesons

Abstract

It is shown that the scattering of neutral mesonsby the spin of the heavy particles (g₂ interaction) on the quantum theory agrees completely in its dependence on energy, scattering angle, and polarisation of the incident and scattered meson with the scattering on the classical theory (neglecting radiation reaction), except for being larger by a constant factor 3, which is due to differences in the averaging over the initial directions of spin of the heavy particle. On the basis of the assumption put forward by Bhabha that the heavy particles can exist in states of all integral charge, it is shown that the scattering of charged mesons by the spin of the heavy particles only differs from the scattering of neutral mesons by factors (1-ΔM² c²/E) and (1-ΔM^-1 c²/E) for scattering by protons and neutrons respectively, ΔM² and ΔM^-1 being the mass excesses of protons of charge 2e and -e over an ordinary proton, and E being the meson energy.Thus on this assumption the scattering of charged mesons shows complete correspondence with the classical theory, and hence the previously given classical formula (36d) taking radiation reaction into account multiplied by a factor 3 will give the scattering of charged mesons up to energies of roughly 10⁹ e.v., correctly to within about 20%. A new formula (36e) is given tentatively which should be more accurate. The scattering of charged mesons on the usual quantum theory shows no correspondence with the classical scattering. The scattering on the basis of Heitler's idea of allowing the heavy particles to exist in higher spin states also shows no correspondence with the classical scattering.